For an in-line slider-crank with crank radius r, rod length L ≥ r and crank angle θ measured from the guide axis, slider position from the crank center is x = r cosθ + √(L² − r² sin²θ). Stroke is exactly 2r.
In-Line Slider-Crank · Exact Position Reference
Explore exact in-line slider-crank position and rod angle with a geometry-preserving animation.
Equation Used
- Crank and connecting rod are rigid.
- Slider axis passes through the crank center.
- Rod length is at least crank radius across the selected domain.
- Clearance, deformation, dynamics, loads and ratings are excluded.
Autoplay advances from the selected reference angle; output cards remain the exact selected reference values.
Rigid crank, rigid rod and constrained slider
The visual preserves the selected crank radius and connecting-rod length at every frame while constraining the wrist pin to the horizontal guide. Autoplay advances from the selected reference angle; the output cards report that selected reference pose.
What the calculator determines
Select crank radius, rod length and reference crank angle. The calculator reports slider position from the crank center, travel from inner dead center, total stroke and signed connecting-rod angle.
Exact in-line closure
x = r cosθ + √(L² − r²sin²θ); travel from inner dead center = x − (L − r); stroke = 2r; α = asin(r sinθ/L).
Selected-input arithmetic
For r = 25 mm, L = 100 mm and θ = 60°, x is about 110.13 mm, travel from inner dead center is about 35.13 mm and stroke is 50 mm.
Kinematics only
The model excludes speed, acceleration, inertia, side thrust, bearing load, friction, clearance, balancing, stress, fatigue, lubrication and ratings.
Questions
Why must L be at least r?
That condition keeps the square-root closure real for every crank angle.
Is slider position measured from dead center?
No. x is measured from the crank center; a separate output reports travel from inner dead center.
References & Further Reading
- Wikipedia contributors. Prismatic joint. Wikipedia
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